Nanosccond time-resolved reflectivity and transmission measurements are used for the observation of solidification phenomena, following incomplete or complete melting of thin Si films (d = 125 nm) by nanosecond laser pulses. Solidification is observed to proceed at the liquid-solid interface as long as the film is not melted completely. On complete melting of the film, nucleation in the liquid becomes important. Heat conduction into the quartz substrate rapidly cools the liquid, until after several tens of nanoseconds homogeneous nucleation of crystalline Si occurs at temperatures around 500 K below the melting point of Si. At even larger supercoolings our measurements indicate the transient formation of amorphous Si in addition to the formation of the crystalline phase.